What is the probability of the random occurrence of a value between 56 and 61 from a normally distributed population with mean 62 and standard deviation 4.5?

Lewis Harvey 2021-01-31 Answered
What is the probability of the random occurrence of a value between 56 and 61 from a normally distributed population with mean 62 and standard deviation 4.5?
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Expert Answer

Laaibah Pitt
Answered 2021-02-01 Author has 98 answers

Step 1
The normal distribution:
A continuous random variable X is said to follow normal distribution with mean μ and standard deviation σ if the probability density function of X is,
f(x)=1σ2πe(xμ)22σ2,<x<,<μ<,σ2>0
Step 2
Finding the probability of the random occurrence of a value between 56 and 61:
The random occurrence of a value (X) follows a normal distribution with mean 62 and standard deviation of 4.5.The required probability is calculated as follows:
P(56<X<61)=P(X<61)P(X<56)
=0.41210.0912=0.3209[Using Excel formula,"NORM.DIST(61,62,4,5,1)""NORM.DIST(56,62,4,5,1)"]

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